In the field of electronic fetal health monitoring, computerized analysis of fetal heart rate (FHR) signals has emerged as a valid decision-support tool in the assessment of fetal wellbeing. Despite the availability of several approaches to analyze the variability of FHR signals (namely the FHRV), there are still shadows hindering a comprehensive understanding of how linear and nonlinear dynamics are involved in the control of the fetal heart rhythm. In this study, we propose a straightforward processing and modeling route for a deeper understanding of the relationships between the characteristics of the FHR signal. A multiparametric modeling and investigation of the factors influencing the FHR accelerations, chosen as major indicator of fetal wellbeing, is carried out by means of linear and nonlinear techniques, blockwise dimension reduction, and artificial neural networks. The obtained results show that linear features are more influential compared to nonlinear ones in the modeling of HRV in healthy fetuses. In addition, the results suggest that the investigation of nonlinear dynamics and the use of predictive tools in the field of FHRV should be undertaken carefully and limited to defined pregnancy periods and FHR mean values to provide interpretable and reliable information to clinicians and researchers.